It is, technically, not a sentence (as traditional grammarbooks use that term†) but a subordinate clause, separated from its head clause by a period to coerce a 'pause' in your reading. (Real Writers write for the ear, not for the eye—and certainly not for grammar teachers.)

Specifically, it is a relative clause headed by which, whose referent is the previous sentence, Della cried. You may paraphrase:

So Della cried—and that led to the thought ...

†It may surprise you to know that many modern grammars do not use the term sentence at all. Sentence is probably best reserved for analysis of written texts, where it means "whatever stretch of words lies between two full stops", those being periods, question marks, and exclamation marks.